Question

If n is a positive integer, what is the remainder when 3^(8n+3)+2 is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Answer 1

Split it up into 3^3.3^(8n) +2

Answer 2

Split the second 3 as (5-2)..expand binomially

Answer 3

didnt gt u

Answer 4

binomial expansion aata hai?

Answer 5

@him1618 if u tak n=1 ans is 4 i want does tis hold true for all n

Answer 6

that isnt the way to do it though

Answer 7

then

Answer 8

how to go abt it

Answer 9

like i said
remodel it as
27 (5-2)^(8n) +2

expand (5-2) part binomially

Answer 10

when u expand it
ull get all terms with a 5 or some power of 5 in them
except fr the last one
so ure left with

27(5q - 2) +2

Answer 11

\(3^{8n}\) if 3 has powers which are divisible by 4, then Remainder it has is 1..
Here : 8n is divisible by 4..

Answer 12

Similary, \(3^3\) will give you 7 as Unit place..

Answer 13

So:

\[3^{8n} \cdot 3^3 + 2 \implies 1 \cdot 7 + 2 \implies 9\]

Answer 14

So, what will you get as remainder when you divide 9 by 5 ??